First things first, don't get too excited about Memphis. It's a city built on industry and although the Downtown area is pleasant enough, I would say that you only need 2 days max there.
In saying that Graceland is awesome, make sure you book the full combo tour which allows access to his cars and planes. You will certainly need the good part of a day to fully appreciate the place (although it can be done much quicker), especially if you go at a peak time. Pre booking will avoid the queue for tickets but you will still have to queue for the actual tour at your allocated time. The system works well and it isn't long before you are on the short bus ride across the street to Graceland itself. I won't go into detail about the tour, it is just amazing and I'm not really old enough to fully appreciate Elvis (my Mum is a huge fan).
Graceland aside there isn't really anything else that is going to take up major time. Beale Street is just ok, the neon is good and of course the music coming out of the bars is great but it is a similar street to the likes of Duval Street in Key West and Bourbon Street in New Orleans, i.e. lots of drunk Americans. We hit a couple of bars but soon got bored.
Sun Studio is a must do if you are an Elvis fan but what surprised me was just how small the place is. Tours are literally half hour in duration and you see the whole studio. It's a memory trip for some people, a must do, but it's not going to need any longer than the allotted tour time and maybe some pictures from the outside. It is also a fair trek from the Downtown area, so if you have a car, great, if not look into public transport because walking there and back would take an age.
Other stuff to consider:-
National Civil Rights Museum
Lorraine Motel (where Martin Luther King was shot)
Court Square is a nice area in Downtown
A ride on the tram which does a loop in Downtown (hardly San Francisco but still good fun)
And that's about it. There is a Zoo and Botanic Gardens as well but we never went, I'm sure they are very similar to other US cities offerings though. Finally, the Memphis Redbirds have a fairly new ballpark near Downtown which might be worth a visit for a game if you fancy see some sport whilst in the city (there are tours also).
I would consider spending some time in Nashville also. A far nicer city and Downtown with some nice buildings and being the home of Country Music, some major attractions dedicated to that genre.
As for a beach to combine with Memphis/Nashville how about somewhere on the Carolinas? Myrtle Beach or my particular favourite Hilton Head. If you do choose Hilton Head you are just one hour drive from Savannah in Georgia, one of the best cities in the whole of the USA.
My itinerary would be something along these lines:-
Fly into Memphis (you will have to connect on a flight from the UK)
2 further nights in Memphis
2 nights Nashville
3 nights in Savannah (you really won't regret it)
and finish up with a week on Hilton Head
HTH